A sinusoidal wave with amplitude 2.00 10 2 cm and frequency 330 Hz is observed t

Question

A sinusoidal wave with amplitude 2.00 102 cm and frequency 330 Hz is observed to be traveling with a speed of 55.0 m/s on a wire held under 200 N of tension.

(a) What is the wave function for this wave in SI units? (Use the following as necessary: x and t. Assume x and y are measured in meters and t is measured in seconds. Do not include units in your answer.)

I thought it should be 0.02sin(37.699x-2073.45t) but it was wrong...

(b) What is the mass per unit length for the wire?

My calculation was 0.07272 but it was wrong.

Explanation / Answer

the genral forn of the waveequation is,

y(x,t)=A*cos(K*x-w*t)

here,

amplitude A=2*10^-2 cm=2*10^-4 cm

A=(0.0002)m

frequency f=330 Hz

angular frequency W=2pi*f

w=2pi*(330)

w=2pi*330

w=2073.45 rad/sec

and

wave speed v=55 m/sec

wave number,K=w/v

k=w/v

k=2073.45/(55)

k=37.7 rad/m

now,

y(x,t)=(0.0002)*cos(37.7*x-2073.45*t)

here,

A,x are in m

t is in sec

b)

tension T=200 N

mass per unit length or linear mass density is u

wave speed v=sqrt(T/u)

55=sqrt(200/u)

==> u=0.066 kg/m

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